chore(release): prepare v0.56.0 release

[Xuanwo]

Which issue does this PR close?

N/A. This PR prepares the v0.56.0 release.

Rationale for this change

The release preparation work had drifted in a few places: version synchronization was incomplete across the core workspace, the release docs referenced the wrong upgrade path, and the changelog plus upgrade notes had not been brought up to date for v0.56.0. This change prepares the release end to end and fixes the tooling gap so future release bumps update the workspace consistently.

What changes are included in this PR?

This updates release-managed versions across core, bindings, and integrations, regenerates dependency manifests, refreshes the v0.56.0 changelog and upgrade notes, and corrects the release documentation checklist. It also fixes dev/src/release/package.rs so just update-version syncs internal workspace package versions and path dependency constraints instead of leaving part of the core workspace behind.

Validation used for this release prep: cargo test --manifest-path dev/Cargo.toml, cargo fmt --check --manifest-path dev/Cargo.toml, cargo metadata --manifest-path core/Cargo.toml --no-deps, and cargo check --manifest-path core/Cargo.toml --workspace.

Are there any user-facing changes?

Yes. The v0.56.0 release metadata, changelog, and upgrade documentation are updated, and the release tooling now keeps internal workspace versions in sync during future version bumps.

AI Usage Statement

AI-assisted: GPT-5 was used to help prepare the release changes and documentation updates.

[PsiACE]

lgtm, can't wait

[suyanhanx]

Let's go!